Adsorption of Aromatics in MFI-Type Zeolites

Delft University of Technology

Adsorption of Aromatics in MFI-Type Zeolites

Experiments and Framework Flexibility in Monte Carlo Simulations

Caro-Ortiz, Sebastián; Zuidema, Erik; Dekker, Desmond; Rigutto, Marcello; Dubbeldam, David; Vlugt, Thijs J.H. DOI 10.1021/acs.jpcc.0c06096 Publication date 2020 Document Version Final published version Published in

Journal of Physical Chemistry C

Citation (APA)

Caro-Ortiz, S., Zuidema, E., Dekker, D., Rigutto, M., Dubbeldam, D., & Vlugt, T. J. H. (2020). Adsorption of Aromatics in MFI-Type Zeolites: Experiments and Framework Flexibility in Monte Carlo Simulations. Journal of Physical Chemistry C, 124(39), 21782-21797. https://doi.org/10.1021/acs.jpcc.0c06096

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Adsorption of Aromatics in MFI-Type Zeolites: Experiments and

Framework Flexibility in Monte Carlo Simulations

Sebastián Caro-Ortiz, Erik Zuidema, Desmond Dekker, Marcello Rigutto, David Dubbeldam,

and Thijs J. H. Vlugt

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ABSTRACT: Computer simulations of adsorption of aromatics in zeolites are typically performed using rigid zeolite frameworks. However, adsorption isotherms for aromatics are very sensitive to small differences in the atomic positions of the zeolite (Chem. Phys. Lett., 1999, 308, 155−159). This article studies the effect of frameworkflexibility on the adsorption of aromatics in MFI-type zeolites computed by grand-canonical Monte Carlo simulations. New experimental data of adsorption of ethylbenzene in a MFI-type zeolite at 353 K is presented. The adsorption of n-heptane, ethylbenzene, and xylene isomers is computed in three MFI-type zeolite structures. It is observed that the intraframework interactions in flexible framework models induce small but important changes in the atom positions of the zeolite and

hence in the adsorption isotherms. Frameworkflexibility is differently “rigid”: flexible force fields produce a zeolite structure that vibrates around a new equilibrium configuration with limited capacity to accommodate to a bulky guest molecule. The vibration of the zeolite atoms only plays a role at high loadings, and the adsorption is mainly dependent on the average positions of the atoms. The simulations show that models for frameworkflexibility should not be blindly applied to zeolites and a general reconsideration of the parametrization schemes for such models is needed.

1. INTRODUCTION

Zeolites are versatile materials that have been used for many different applications. The use of zeolites ranges from water cleaning,1,2catalyst for the refining industry,3to the capture of radioactive particles,4among other applications.5−8Knowledge of the adsorption behavior of hydrocarbons in the pores of zeolites is important for the understanding of the catalytic activity of the zeolite.9−11 Many industrial processes, such as the separation of xylenes, disproportionation of toluene, ethylbenzene dealkylation, strongly rely on the interaction of hydrocarbons within a zeolite.12−15

Zeolites are commonly considered as very rigid structures as its atomic bonds and angles are highly constrained.16,17 An inflection point in the adsorption isotherm reflects either that molecules start to fill a new adsorption site18,19 and/or that there is a structural change in the zeolite due to the number of adsorbed molecules20−22 or the temperature.23,24 Adsorption of aromatics in MFI-type zeolites is a typical example of a mix of such factors.25Talu et al.20 described the isotherm shapes for benzene, toluene, and p-xylene adsorbed in MFI-type zeolites. It is reported that, with increasing temperature, the isotherm shape changes from type IV to type I.20 The observable kink in the isotherm at lower temperatures disappears at temperatures higher than 80°C.20The all-silica

form of the MFI-type zeolite (silicalite) is known to show a monoclinic or orthorhombic structure depending on the temperature and loading.26,27 Van Koningsveld et al.28 identified three structures of the p-xylene/silicalite system: Mono (monoclinic), Ortho (orthorhombic) and Para (also orthorhombic). Very small structural differences are observed between the Ortho and Para lattices.29The silicalite/p-xylene system is known to have the Ortho structure when the loading is lower than 4 molec./uc.28At 8 molec./uc, the silicalite/p-xylene system shows the Para structure.26 Sacerdote et al.30 reported that silicalite loaded with benzene, toluene, or ethylbenzene shows a Mono structure for loadings lower than 4 molec./uc. Sorenson et al.31 reported that benzene loading does not cause a significant change in the unit cell volume of silicalite. o-Xylene and m-xylene do not access nor cause significant deformations to the zigzag channels relative to the room-temperature empty Mono framework.32 o-Xylene is

Received: July 3, 2020 Revised: August 21, 2020 Published: September 9, 2020

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located exclusively in the intersections of the channels at 273 and 315 K.33 Several experimental studies that describe the adsorption of aromatics in MFI-type zeolites can be found in the literature.20,26,30,32−45

The adsorption of aromatics in MFI-type zeolites has also been studied by molecular simulations. Commonly, Monte Carlo (MC) simulations in the grand-canonical ensemble (GCMC) are used to compute sorbate loadings as a function of temperature and pressure in a zeolite framework.46−48 Several studies where MC is used to investigate adsorption of aromatics in MFI-type zeolites can be found in the literature.49−62Snurr et al.49computed adsorption isotherms of benzene and p-xylene in MFI-type zeolites. Large differences in the loadings are found when using the MFI Ortho and Para structures. It is shown that, below 4 molec./uc, benzene and p-xylene are adsorbed in the intersections of the Ortho structure. Molecules in the intersections are too far apart to strongly interact with each other. The molecules are also located in the channels at higher loadings, allowing sorbate/sorbate inter-actions.49 Torres-Knoop et al.51 reported simulations of adsorption of ethylbenzene and styrene in the Para form of MFI-type zeolite at 433 K. It is observed that, close to saturation conditions, styrene can be located in the zigzag channel. At the same conditions, ethylbenzene suffers from size exclusion effects. Therefore, it is located exclusively in the intersections of the channels. Mohanty et al.52 reported GCMC simulations of p-xylene and m-xylene in silicalite. These authors found that p-xylene adsorption selectivity over m-xylene is due to the difficulty of m-xylene to access the adsorption sites of the framework in comparison to p-xylene. The large energetic difference between p-xylene and m-xylene is the primary reason for p-selectivity.

Computer simulations of the adsorption of hydrocarbons in zeolites are typically performed using rigid zeolite frame-works.46,63,64 Clark and Snurr65 performed simulations of the adsorption of benzene in the Ortho and Para structures of silicalite at 343 K. The simulations showed that the computed loadings are very sensitive to small differences in the atom positions of the zeolite. It is found that the Henry coefficient of benzene in the Ortho structure described by Olson et al.66is 3.1 times larger than in the Ortho structure described by van Koningsveld et al.67The mean and maximum differences of the atomic positions of these two Ortho structures are only 0.11 and 0.41 Å, respectively. It is suggested that interactions that include lattice flexibility and polarizability are required to simulate systems where moleculesfit tightly in the pores.65,68 Only a limited amount of studies have approached the simulations of adsorption using a flexible zeolite framework. Garci ́a-Pérez et al.69 _{and Sánchez-Gil et al.}70

studied argon adsorption in MFI and MEL, respectively.71 described the loadings of methane in LTA. Fang et al.72 considered framework flexibility for the adsorption of CO2 in an ammonium MFI-type zeolite. It is observed that the overall effect of framework flexibility is small for the adsorption of CO₂in the zeolite structure. Vlugt et al.63,67reported the effect offlexibility in the adsorption of n-alkanes and cycloalkanes in a MFI-type zeolite. It is found that for molecules with an inflection behavior in the isotherm, the influence of the flexibility seems to be larger than for molecules without such inflection. The influence of the flexibility on the adsorption of cyclohexane is similar to n-alkanes.73

Frameworkflexibility has also been studied in other porous materials.74−80Witman et al.81studied the effect of framework

flexibility on the separation of Xe/Kr mixtures in ∼3000 metal−organic frameworks (MOFs). A model that predicts the Henry regime adsorption of each framework and selectivity as a function of frameworkflexibility is used. The results of this study suggest that the selectivity of the Xe/Kr mixtures can be increased or decreased up to two orders of magnitude when unit cell volume changes are allowed.81 Agrawal and Sholl82 examined the adsorption of nine molecules and four mixtures in 100 MOFs. It is observed that adsorption selectivities can be significantly affected by framework flexibility. It is suggested that including framework flexibility is important when attempting to make quantitative predictions of adsorption selectivity in MOFs. Heinen and Dubbeldam83review in depth the prospects of development of force fields for framework flexibility in MOFs. In this review, it is shown that there is an urgent need for efficient sampling schemes that capture stimuli-driven phase transitions. This limits the predictive capacity of existing force fields for framework flexibility in MOFs.83

This article explores how the inclusion of framework flexibility in a model affects the adsorption of aromatic hydrocarbons in type zeolites. Structural changes of MFI-type zeolites (i.e., Mono to Ortho/Para transition) imply small geometry and volume changes in the framework unit cell31,84 that are not considered in this work. Instead, framework flexibility aims to study local changes of the MFI-type zeolite framework induced by the presence of guest molecules. Computations of adsorption of n-heptane, ethylbenzene, and xylene isomers are performed in three MFI-type zeolite structures. Several models are considered to describe the flexibility of the zeolite framework. The simulations of n-heptane adsorption aim to investigate if the details of framework flexibility play any role on a system known to be well reproduced with a rigid zeolite structure.85Experimental data of adsorption of ethylbenzene in a MFI-type zeolite at 353 K is presented. The new experimental data shows higher loadings than in previously reported isotherms in the literature. Pore size distributions are computed to investigate the effect that framework flexibility induces in the MFI-type zeolite structures. The experimental and simulation procedure are explained inSection 2. The results of experiments, computed pore-size distributions, and computed loadings are reported and discussed inSection 3. It is shown that the intraframework interactions in flexible framework models induce small but important changes in the atom positions of the zeolite and hence in the adsorption isotherms. The current challenges to model and predict reliable molecular insights about the system are also discussed in Section 3. Our concluding remarks regarding the influence of the force fields for framework flexibility on the adsorption of aromatics in MFI-type zeolites are discussed inSection 4.

2. METHODS

2.1. Experimental Procedure. Large-crystal ZSM-5 samples with silica-to-alumina ratios of around 80 are synthesized according to established literature procedures.86 Vapor-phase adsorption isotherms are measured using the volumetric technique on a Micromeritics 3Flex physisorption analyzer. A vapor reservoirfilled with ethylbenzene is held at constant temperature at 30°C through a heating mantle. The adsorbate is purified using the freeze−pump−thaw method to evacuate non-condensed species. The vapor reservoir is immersed in a cryogenic bath. Nitrogen and oxygen are not

condensed at the pressures of the purification process. Nitrogen and oxygen are removed by evacuation. After purification, the sample is maintained at 30 °C. The vapor pressure is determined for this temperature.

About 150−500 mg of the adsorbent powder is placed in a glass sample tube. The zeolites are pre-dried for at least 4 h in vacuum at 450°C in a Micromeritics SmartVac. The samples are activated in situ in the 3Flex device by increasing the temperature to 450°C at a heating rate of 10 °C/min under vacuum. The heating mantle is removed and replaced by an external thermostatic bath, maintaining the obtained vacuum (<5× 10−5mmHg).

The adsorption isotherms are determined at 80 °C by pressure-controlled dosing of the adsorbate. The partial pressures are increased up to approximately 0.7 P(80°C)/ P0(30°C). The adsorbate is dosed atfixed amounts of 0.2 cm3/g STP for pressures lower than 0.03 mm Hg. For pressures higher than 0.03 mm Hg, the pressure is increased by afixed pressure rate of 0.1 mm Hg. The equilibration interval is set at 180 s.

2.2. Simulation Procedure. The adsorption computations are performed using the Continuous Fractional Component Monte Carlo (CFCMC)87,88algorithm in the grand-canonical ensemble. The RASPA software89−91 is used for all simulations. Periodic boundary conditions are applied to a simulation box consisting of 2× 2 × 3 unit cells of MFI-type zeolite. The all-silica structures described by van Koningsveld et al. (Mono,84 Ortho,67 and Para28) are considered. The adsorption of aromatics is computed for the three structures. The Ortho structure is used for n-heptane adsorption simulations. A cutoff radius of 14 Å is applied for all Lennard-Jones (LJ) interactions, and analytic tail corrections are used.92,93 The interactions between different atom types are obtained using Lorentz−Berthelot mixing rules.92 The Ewald summation94with a relative precision of 10−6is used to account for the long-range electrostatic interactions. In the CFCMC algorithm, the interactions of a fractional molecule are scaled by theλ parameter in the range of 0−1 (0 for no interactions with surrounding molecules/framework and 1 for full interaction with surrounding molecules/framework).

A MC cycle is the maximum between 20 and N-move-attempts, with N being the number of molecules in the system.89 At each MC cycle, trial moves attempt to rotate, displace, randomly reinsert, and insert adsorbates. Also, λ-moves scale the interactions of the fractional molecule (via the CFCMC algorithm87,88). The simulations are started with 100,000 MC cycles to initialize the system. The initialization run only allows translation, rotation, and insertion moves. After that, a stage of 400,000 MC cycles is used to equilibrate the system. All the considered types of trial moves are allowed, and the biasing factors for theλ-moves of the CFCMC algorithm are calculated.λ-Moves are biased to obtain a flat λ probability distribution. The use of this move is advantageous as it enables an efficient insertion and deletion of sorbate molecules in the system.95,96Ensemble averages are obtained in a 500,000 MC cycles production stage. The reported errors account for the 95% confidence interval calculated by dividing the production run into five parts. An extra MC trial move is included to simulate aflexible zeolite framework, which attempts a random displacement to a randomly selected zeolite atom.63Since the volume of the simulation box is fixed, the equilibrium framework density is not affected by framework flexibility.

Force fields that model the flexibility of the zeolite framework (host−host interactions) are commonly based on the description of vibrational properties, such as the infrared spectra of the zeolite atoms,97,98 and/or ab initio quantum chemical calculations.99,100 Several force fields for framework flexibility have been reported in the literature.16,99−107

Such forcefields are typically used in the calculations of diffusion of aromatics in MFI-type zeolites by molecular dynamics simulations.108−110 Some sets of zeolite intraframework interactions only include harmonic potentials between the zeolite atoms, while others also add a combination of LJ and partial charges. Polarization of the zeolite atoms can also be added by using the core−shell method.111 In this method, typically the oxygen atoms of the zeolite are separated into cores and shells.112−114Phase transitions and negative thermal expansion can be studied using this method.74The predicted crystal structures agree very well with crystallographic data from experiments.115 The core−shell model requires formal charges that are higher than the partial charges based on ab initio calculations.74 The computational time using this method is increased due to the use of more particles in the system.74

The Nicholas105 model, the Demontis103 model, and the model reported by Jeffroy et al.16

are considered for investigating the host−host force field induced effects in MFI-type zeolite frameworks. The force field parameters are listed in the Supporting Information. The Demontis model102−104 consists on describing the flexibility of the zeolite only by Si−O bond stretching and O−Si−O Urey− Bradley potentials. The Nicholas model105 includes intra-molecular (1−4) LJ and electrostatic interactions besides torsional, bond-bending, and bond-stretching potentials. The model by Jeffroy et al.16 is a transferable force field able to predict the structure of zeolites including extra-framework cations. The host−host interactions are determined by electrostatic interactions, bond-stretching, and bond-angle parameters.

There is a distribution of bond lengths and angles in MFI-type structures from crystallography.26,67,84 The Nicholas model, the Demontis model, and the model by Jeffroy et al. use constant equilibrium bond lengths and angles. The so-called modified form of these models take the equilibrium bond lengths and bond angles (in the Urey−Bradley term) directly from the crystallographic structure to which the model is applied.63 As discussed in the following section, this modification is used to avoid large deviations from the experimental crystal structure. In this work, the modified Nicholas105 model and the modified Demontis103 model are used for the simulations of adsorption of aromatics.

To take into account the effect that the host−host interactions have on the zeolite structure, an optimization of the atom positions of the zeolite framework at 0 K with the flexible force field is performed. The structure with atom positions optimized is obtained using the mode-following minimization method116,117 for each initial experimental zeolite topology subject to the host−host force field. The pore-size distribution (PSD) of the structures with atom positions optimized at 0 K using each host−host force field is calculated geometrically with the method of Gelb and Gubbins.118,119 The MFI-type zeolite atom positions are optimized at 0 K with the Demontis model,103 the Nicholas model,105and the model reported by Jeffroy et al.16as well as the modified forms of each force field. The PSD is also

calculated for each of the MFI-type zeolite lattices from crystallographic data. Henry coefficients of ethylbenzene in the MFI-type structures are calculated via the Widom test-particle insertion method.120

The interactions between the zeolite and guest hydro-carbons (host−guest interactions) are described using several force fields.121−127 The host−guest force fields are usually obtained byfitting the parameters to experimental data,10such as adsorption isotherms. The TraPPE-zeo model126is used in this work. In this forcefield, all oxygen and silicon atoms are modeled with Lennard-Jones interactions and partial charges. The development of this forcefield is focus on transferability and variety of zeolite/guest systems.126 As such, it isfitted to match the experimental adsorption isotherms of n-heptane, propane, carbon dioxide, and ethanol in zeolites. The partial charges of the zeolite atoms are a critical parameter for the force fields and adsorption.128,129 Typical partial charges for silicon atoms have been reported in the range of +0.5 to +4 e.130 The host−guest electrostatic interactions from TraPPE-zeo126(+1.5 and−0.75 e for Si and O, respectively) are fitted consideringfixed positions of the zeolite atoms. Zeolite host− host interactions that include electrostatics are likely to be incompatible with a guest−host force field that also includes electrostatics. The combination of two types of forcefields can be cumbersome. The Nicholas model, the Demontis model, and the model reported by Jeffroy et al. use different partial charges for the zeolite atoms than the TraPPE-zeo126 force field. In this work, the electrostatic interactions of the zeolite atoms are modeled by each host−host force field used in the simulation. The partial charges are listed in the Supporting Information.

Molecular simulations of aromatics typically use forcefields (guest−guest interactions) that model the vapor−liquid equilibrium (VLE) with LJ potentials or a combination of LJ and electrostatic interactions.131,132 In the case of aromatic species, a common practice in the development of these force

fields is to fit the interaction parameters to reproduce the VLE of the pure components133−139 or by ab initio quantum mechanical calculations.140−143

Despite the extensive use of guest−guest force fields that use electrostatic interactions (such as OPLS138,139) for the simulation of adsorption of aromatics in zeolites,49,51,53,144 the electrostatic interactions arefitted for VLE and not for the interaction with a host framework. In this work, the electrostatic interactions of the zeolite atoms are modeled by each host−host force field used in the simulation. Such electrostatic interactions are not suited for the interaction with an adsorbate but for the zeolite framework with itself. Therefore, it is convenient to use a guest−guest force field that does not explicitly use partial charges for electrostatic interaction. The uncharged TraPPE-UA145,146 force field is chosen for the guest−guest interactions. The TraPPE-UA is a widely used forcefield that is designed to reproduce the VLE of alkylbenzenes and n-alkanes, among other chemical species. The united atom approach is used by merging a carbon atom and its bonded hydrogen atoms into a single uncharged interaction site representing each CHxgroup in the n-alkanes and aromatic species. Aromatics are modeled as rigid molecules, except ethylbenzene, that includes a torsional potential in the CH3−CH2−CH bond angle. The force field parameters are listed in theSupporting Information.

3. RESULTS AND DISCUSSION

3.1. Force Field Induced Effects in MFI-Type Structures. The effect of each host−host force field on the zeolite pores can be observed in the pore-size distribution. The PSD of MFI-type zeolite structures with atom positions optimized at 0 K using the Demontis103 model, the Nicholas105model, and the model reported by Jeffroy et al.16 are calculated. The PSDs are compared with the PSD computed for each experimental crystal structure. The modified form of each force field is also included. As an

Figure 1.Minimum-energy atomic configuration of MFI Para structures with atom positions optimized at 0 K using the modified Demontis model (left) and the original Demontis103model (right). The minimum-energy structure exactly reproduces the experimental crystal structure28when using the modified Demontis model. The blue ring is the same in both structures. The blue ring highlights differences in the atomic position and the change of shape of the straight channel caused by the use offixed equilibrium bond lengths with the original Demontis model.

example,Figure 1shows the visible differences in the MFI Para structure when using constant equilibrium bond lengths in the Demontis model compared to the modified Demontis model. For the modified Demontis model, the experimental crystal structure is exactly reproduced when T → 0 K. With the original Demontis model, atomic positions are shifted and the shape of the straight channel changes to an oval shape.Figure 2shows the Si−O bond length distribution of the MFI Para

structure from crystallography28 and the MFI Para structure with atom positions optimized at 0 K using the original Demontis model. The Si−O bond lengths of MFI Para structure from experiments28 range from 1.58194 to 1.61089 Å. The Si−O bond length distribution of the MFI Para structure with atom positions optimized using the original Demontis model ranges from 1.60398 to 1.60427 Å. Thefixed equilibrium bond lengths of the original Demontis model significantly reduce the bond length range. The shape and atom position changes shown inFigure 1are caused by the use offixed equilibrium bond lengths and angles and the reduction of the bond length range. All crystal structures are available in CIF format in theSupporting Information.

The PSD of MFI-type zeolite structures with atom positions optimized at 0 K using the Demontis103 model, the Nicholas105model, and the model reported by Jeffroy et al.16 are shown inFigure 3. In a PSD of MFI-type zeolites, the peak centered at a diameter of approximately 4 Å corresponds to the zigzag and straight channels. The peak centered at a diameter of approximately 5.5 Å corresponds to the intersection of the channels. Using the Demontis model, significant differences can be observed in the PSD of the Ortho structure. The PSD shows a new peak at a diameter smaller than 4 Å, suggesting that the channels decreased its size. This change in the structure is exclusively related to the use of constant bond lengths and angles. In the Mono and Para structures, the shift of the peak shows that the intersections are smaller.

When the Nicholas model and its modified form are used, the PSDs of the Mono structure do not show significant deviations from the experimental structure. The Nicholas model and the modified form induce an expansion of the intersections in the Ortho structure. The peak corresponding

to the intersection is shifted approximately +0.5 Å. In the Para structure, the peaks corresponding to the intersections and the channels are shifted approximately 1 Å. This means that the pores are significantly larger than in the Para structure from experiments. As the original and modified forms of the Nicholas model show similar shifts of the pore-size peaks, these shifts can be related to the LJ and the strong electrostatic interactions accounted in the optimization of the atom positions with the forcefield.

The model presented by Jeffroy et al.16 _{induces significant}

differences in the Ortho structure. The channels are smaller, while the intersections are expanded. The peak corresponding to the channels is shifted approximately −0.5 Å. The peak corresponding to the intersections is shifted approximately +0.5 Å. In addition, the intersections of the Para structure approximately 0.5 Å (in diameter) larger than in the crystal structure from experiments. The modified form of this model shows better agreement with the PSD of the experimental Mono and Ortho structures. A mean displacement of 0.462 Å of the atoms in the Para structure suggest that the zeolite structure is significantly influenced by the force field.

Table 1lists the mean and maximum displacements atomic

position induced by each of the host−host force fields and the Henry coefficient of ethylbenzene at 353 K in the MFI-type structures. The displacements suggest that taking the equilibrium bond distances and angles from the experimental crystal structure reduces the deformation induced by the host− host force field in the structure. Clark and Snurr65 observed that a mean displacement of 0.11 Å of the zeolite atoms is enough to significantly influence the adsorption of benzene in MFI-type zeolites. In this work, all mean displacements accounted in the optimized structures at 0 K with the modified forms of the forcefields are higher than 0.11 Å (except for the modified Demontis model). Henry coefficients of ethylbenzene significantly vary within MFI-type zeolite structures. For the crystal structures from experiments, the Henry coefficients of ethylbenzene in the Mono and Ortho structure are similar and larger than in the Para structure.

Significant differences can be observed using the modified and original host−host force fields. For the original Demon-tis103 model in the Para structure, the Henry coefficient of ethylbenzene is 3.4 times smaller than when taking the equilibrium bond lengths directly from the crystal structure from experiments in the modified Demontis model. This suggests that Henry coefficients (and hence adsorption) of ethylbenzene in MFI-type zeolites are very sensitive to small deviations in the atom positions of the zeolite framework.

3.2. Adsorption of n-Heptane in MFI-Type Zeolite. The adsorption of n-heptane in MFI Ortho at 303 K is calculated with the modified Nicholas105 model, the rigid framework with atomic positions fixed to the crystal from experiments,67 and the rigid framework with atom positions optimized at 0 K using the modified Nicholas105model. The adsorption isotherms are shown inFigure 4. Experimental data from Sun et al.147is included. The simulation results by Vlugt and Schenk63 are included. The simulation by Vlugt and Schenk63 were performed using a modified Demontis-like model, by tuning the spring constants k/kB = kO− O/kB = 0.2kSi− O/kB, from 6000 to 100000 KÅ−2 (original Demon-tis103 model: kO− O/kB = 51831.61 KÅ−2). The simulations using the rigid framework slightly underestimate the amount of adsorbed molecules when the loading is higher than 4 molec./ uc. Using the rigid structure with atom positions optimized at

Figure 2.Si−O bond length distribution of the MFI Para from the structure from experiments28 and from the MFI Para minimum-energy structure obtained optimizing the atomic positions at 0 K using the Demontis103model. The original Demontis103model uses fixed equilibrium Si−O and O−(Si)−O bond lengths. The Si−O bond length distribution of the MFI Para structure with atom positions optimized at 0 K with the modified Demontis model exactly reproduces the Si−O bond length distribution from experiments.

0 K using the modified Nicholas model, the experimental loadings are slightly overpredicted. These differences between the loadings in the rigid and the rigid structure with atom

positions optimized at 0 K are related to the pore size changes induced by the modified Nicholas model. The loadings computed using the modified Nicholas model are close to

Figure 3. Pore-size distributions (PSDs) of MFI-type zeolite structures optimized at 0 K with the flexible host−host models. Experiments correspond to the PSD computed in lattices from experiments (Mono,84Ortho,67and Para28). PSD of the MFI (a) Mono, (c) Ortho, and (g) Para structures with atom positions optimized at 0 K using the Demontis103model. PSD of the MFI (b) Mono, (e) Ortho, and (h) Para structures with atom positions optimized at 0 K using the original and the modified Nicholas105 model. PSD of the MFI (c) Mono, (f) Ortho, and (i) Para structures with atom positions optimized at 0 K using the original and modified model by Jeffroy et al.16In a PSD of MFI-type zeolites, the peak centered at a diameter of approximately 4 Å corresponds to the channels. The peak centered at a diameter of approximately 5.5 Å corresponds to the intersection of the channels.

Table 1. Mean and Maximum Displacement (Å) of the Atomic Positions between the Experimental MFI-Type Structures, the Rigid Structure with Atom Positions Optimized at 0 K Using the Host−Host Force Fields, and the Modified Formsa

Mono Ortho Para

mean (Å) max (Å) K_H,eb(mmol/kg Pa) mean (Å) max (Å) K_H,eb(mmol/kg Pa) mean (Å) max (Å) K_H,eb(mmol/kg Pa)

Demontis103 0.211 0.582 14.9(11) 0.282 0.679 13.9(5) 0.315 0.786 3.6(3)

Mod. Demontis103 _{0.000 0.000 24.3(11) 0.000 0.000 26.1(24) 0.000 0.000 12.3(8}

Nicholas105 0.216 0.511 24.6(13) 0.229 0.497 30.9(15) 0.455 1.081 25.8(9)

Mod. Nicholas105 0.164 0.449 30.3(10) 0.189 0.536 44.2(15) 0.342 0.611 31.1(9)

Jeffroy et al.16 _{0.271 0.658 9.8(3) 0.419 1.065 10.8(4) 0.475 1.238 13.2(4)}

Mod. Jeffroy et al. 16 0.137 0.311 29.8(13) 0.226 0.656 27.8(20) 0.462 1.109 22.4(11)

a_K

H, ebis the Henry coefficient of ethylbenzene at 353 K in the MFI-type structures with atom positions optimized at 0 K using the host−host force

fields and the modified forms. The Henry coefficient of ethylbenzene in the MFI-type structures with atom positions optimized at 0 K using the modified Demontis103_{model correspond to the Henry coefficient in the crystal structure from experiments. The numbers in parentheses denote the}

the experimental loadings. The isotherm computed using the modified Nicholas model is in excellent agreement with the predictions of Vlugt and Schenk.63 All simulations under-estimate the experimental loadings at high pressures. All simulated isotherms converge to the same maximum loading of approximately 6.5 molec./uc. in the studied pressure range. The simulations suggest that there is marginal contribution of theflexibility models in the prediction of n-heptane loadings in MFI-type zeolites as the differences are small and below the statistical uncertainties of the simulations.

3.3. Adsorption of Ethylbenzene in MFI-Type Zeolites. Figure 5 shows the adsorption isotherm of

ethylbenzene in MFI-type zeolites (Si/Al ratio: 80) at 353 K, experimentally obtained in this work. The experimental loadings obtained in this work are listed in the Supporting

Information. The adsorption of ethylbenzene in MFI-type

zeolites has been reported by Song et al.40 at 345 K (Si/Al ratio: 1338) and Schumacher and Karge35 at 355 K (Si/Al ratio: 34). Type I isotherms are reported with a maximum loadings of approximately 4 and 3.5 molec./uc, respectively.

Choudhary and Srinivasan148reported the effect of the Si/Al ratio in the adsorption of benzene in MFI-type zeolites at 523 K. It is observed that the loadings of benzene increase with the decrease in the Si/Al ratio. Guo et al.149indicate that the pore size of MFI-type zeolites become smaller with increasing Si/Al ratios of the framework. This suggest that the loadings of ethylbenzene from this work are expected to be higher than the loadings reported by Song et al.40and lower than the loadings reported by Schumacher and Karge35due to differences in the Si/Al ratio of the zeolites. In this work, loadings over 4 molec./ uc are observed at pressures higher than 40 Pa. The loadings reached 5 molec./uc at approximately 800 Pa. The maximum loading obtained is 5.21 at 1211 Pa in sample A. The loadings obtained in this work are higher than the loadings reported in the literature.35,40This suggest that the differences between the loadings obtained in this work and the isotherms from literature35,40 are not related to Si/Al ratio differences. The experimental data from this work suggests that the channels of MFI-type zeolites are able to host ethylbenzene molecules when the intersections are loaded at 353 K.

The adsorption of ethylbenzene in MFI-type zeolites at 353 K is calculated using the modified Nicholas model, the modified Demontis model, the rigid experimental lattice, and the rigid framework with atom positions optimized at 0 K with the modified Nicholas model in the Mono, Ortho, and Para MFI-type structures. The adsorption isotherms (Si/Al ratio: ∞) and the experimental data (Si/Al ratio: 80) are shown in

Figure 6. Experimental observations reported that the MFI/

ethylbenzene system is in the Mono structure when the loading is lower than 4 molec./uc.26

All simulations using the modified Demontis model reach approximately 4 molec./uc at the high pressure in the considered pressure range. All the molecules are located in the intersections of the channels.

For the Mono and Ortho structures, framework flexibility using the modified Demontis model does not show any contribution to the loadings compared to the use of the rigid frameworks from crystallography. In the case of the Para structure, the loadings obtained with the modified Demontis model are lower than in the rigid structure at high pressures.

In the Mono structure, the use of the modified Nicholas model does not show any influence of the framework flexibility when the loading is lower than 4 molec./uc compared to the rigid structures. The ethylbenzene loading in the rigid structure with atom positions fixed to the crystal structure from experiments and the rigid structure with atom positions optimized at 0 K both reach 4 molec./uc in the considered pressure range. At 2000 Pa, a loading of approximately 0.5 molec./uc higher than in the rigid frameworks are obtained. At pressures higher than 200 Pa, loadings higher than 4 molec./uc are obtained with the modified Nicholas model. When using the modified Nicholas model, the framework flexibility plays a role when loadings are higher than 4 molec./uc.

In the Ortho structure, the simulations using the modified Nicholas model and the rigid structure with atom positions optimized at 0 K predict higher loadings than in the rigid framework from crystallography. Ethylbenzene loadings reach approximately 4 molec./uc with the rigid frameworks and slightly higher loadings with the modified Nicholas model. In the Para structure, ethylbenzene loadings are similar when using the modified Nicholas model and the rigid structure with atom positions optimized at 0 K for pressures up to 100 Pa. At 2000 Pa, the simulations with the modified Nicholas model

Figure 4.Adsorption isotherm of n-heptane in MFI Ortho at 303 K. Experimental data from Sun et al.147 Closed symbols denote the experimental data. Crossed symbols denote the simulations by Vlugt and Schenk.63Open triangles, circles, and squares denote simulations using the modified Nicholas105_{model, the rigid structure with atom}

positions optimized at 0 K with the modified Nicholas model, and the rigid crystal structure from experiments,67respectively.

Figure 5.Experimental adsorption isotherm of ethylbenzene in MFI-type zeolite samples (Si/Al ratio: 80) at 353 K. Sample A and B are obtained in this work. Experimental data of ethylbenzene adsorption in MFI-type zeolites by Song et al.40at 345 K (Si/Al ratio: 1338) and Schumacher and Karge35 at 355 K (Si/Al ratio: 34) are included. Experimental data are listed in theSupporting Information.

predict loadings 0.5 molec./uc higher than in the rigid frameworks. At high pressures, the loadings in the rigid and the rigid structure with atom positions optimized at 0 K are the same. A typical snapshot of the simulation of adsorption in MFI Para using the modified Nicholas model at 353 K and 2000 Pa is included in theSupporting Information. It can be observed that ethylbenzene molecules are located in the channels and in the intersections of the channels.

Obtaining higher loadings in the rigid structure with atom positions optimized at 0 K than in the rigid structure from experiments suggests that the atomic configuration of the optimized structure at 0 K can be related to the pore-size

difference shown in Figure 3h. The intersection of the rigid structure with atom positions optimized at 0 K using the modified Nicholas model are approximately 0.5 Å larger than in the rigid crystal structure from experiments.

Comparing the Mono, Ortho, and Para systems, higher maximum loadings are obtained in the Para structure for all cases. The adsorption of molecules in the Mono structure is less affected by use of the modified Nicholas model at low loadings. There is a qualitatively good agreement between the simulations using the modified Nicholas model and the experimental data. For loadings lower than 4 molec./uc, the simulations using the Mono structure are in good agreement with the experiments, and theflexibility does not play a role in this regime. The loadings computed in the MFI Mono rigid structure with atom positions optimized at 0 K are closer to the experimental loadings than with the rigid structure. At loadings higher than 4 molec./uc, the simulations in the Para structure using the modified Nicholas model show a better agreement with the experiments than using the rigid frameworks and the modified Demontis model.

3.4. Adsorption of Xylene Isomers in MFI-Type Zeolites. The adsorption of xylene isomers in MFI-type zeolites at 373 K is calculated with the modified Nicholas model, the modified Demontis model, the rigid framework and the rigid structure with atom positions optimized at 0 K with the modified Nicholas model. The adsorption isotherms are shown inFigures 7, 8, and9. For m-xylene (Figure 7) in the Mono structure, framework flexibility does not influence the isotherm. The differences in the loadings using the modified Nicholas model, the modified Demontis model, the rigid structure from experiments and the rigid structure with atom positions optimized at 0 K are below the statistical error of the simulations. In the Ortho structure, the highest loadings are predicted in the rigid structure with atom positions optimized at 0 K. At 800 Pa, all simulations predict a loading of approximately 4 molec./uc. In the Para structure, the modified Nicholas model and the rigid structure with atom positions optimized at 0 K using the modified Nicholas model predict higher loadings than in the rigid structure from experiments and with the modified Demontis model. This suggests that obtaining higher loadings with the modified Nicholas model is due to the deformation of the crystal structure (in the structure with atom positions optimized at 0 K) instead of the vibrations of atoms. In the m-xylene/MFI-type zeolite system, the flexibility of the zeolite does not play a large role in the adsorption. All simulations of adsorption of m-xylene in the MFI-type zeolites overestimate the experimental data.

For o-xylene (Figure 8), the loadings predicted with the modified Nicholas model and the rigid structure with atom positions optimized at 0 K using the modified Nicholas model are higher than in the rigid structure for each MFI-type zeolite lattice. A very small influence of the flexibility of the modified Nicholas model can be observed for each structure. The computed loadings differ within the statistical error with the rigid structure with atom positions optimized at 0 K using the modified Nicholas model. The loadings obtained with the modified Demontis model are lower than in the rigid structure from experiments.

It is important to note that the loadings from experiments of adsorption in silicalite36at 373 K for m-xylene are much lower than those reported for o-xylene. The loadings reported by Wu et al.36at 293 K show higher loadings for m-xylene than for

o-Figure 6.Adsorption isotherms of ethylbenzene at 353 K computed for the (a) Mono, (b) Ortho, and (c) Para structures (Si/Al ratio: ∞). Closed symbols denote the experimental data from this work (Si/ Al ratio: 80). Open triangles, upside down triangles, circles, and squares denote the simulations with the modified Nicholas105model, the modified Demontis103 model, the rigid structure with atom positions optimized at 0 K using the modified Nicholas model, and the rigid structure from experiments, respectively.

xylene in silicalite. This suggests that the loadings of m-xylene at 373 K in silicalite can be hindered by slow diffusion.

The modified Demontis model yields loadings closer to the experimental data than any of the models here considered.

For p-xylene (Figure 9) in the Mono and Ortho structures, the modified Nicholas model predicts higher loadings than the rigid structures only at 800 Pa. At lower pressures, the differences are below the statistical uncertainties of the simulations. The modified Demontis model predicts the lowest loadings in all MFI-type zeolite structures. The loadings obtained with the modified Demontis model are lower than in the rigid structure from experiments. The modified Demontis model yields loadings in excellent agreement with the

experimental isotherm. In the Para structure, the loadings computed in the rigid structure from experiments are higher than with any flexible model considered. The modified Nicholas model yields loadings close to the rigid structure with atom positions optimized at 0 K, which suggests that the flexibility does not play a role in this case. The large differences between the loadings in the rigid structure from experiments and with the modified Demontis model at high pressures suggests that the adsorption of molecules in the intersections of the Para structure is affected by the displacement of the zeolite atoms.

3.5. Discussion. The simulations from this work under-score the difficulties in modeling the framework flexibility and

Figure 7.Adsorption isotherms of m-xylene at 373 K computed in the (a) Mono, (b) Ortho, and (c) Para structures. Closed symbols denote the experimental data from Wu et al.36Open triangles, upside down triangles, circles, and squares denote the simulations with the modified Nicholas105 _{model, the modified Demontis}103 _{model, the}

rigid structure with atom positions optimized at 0 K using the modified Nicholas model, and the rigid structure from experiments, respectively.

Figure 8.Adsorption isotherms of o-xylene at 373 K computed in the (a) Mono, (b) Ortho, and (c) Para structures. Closed symbols denote the experimental data from Wu et al.36Open triangles, upside down triangles, circles, and squares denote the simulations with the modified Nicholas105 _{model, the modified Demontis}103 _{model, the}

rigid structure with atom positions optimized at 0 K using the modified Nicholas model, and the rigid structure from experiments, respectively.

the adsorption of aromatics in MFI-type zeolites appropriately. Models able to describe the phase transitions that MFI-type zeolites show in experiments such as core−shell are difficult to combine with adsorbate models to study adsorption.74 Also, the use of a core−shell model implies a significant increase in the number of particles in the system, which reduces the efficiency of the simulation.74 For modeling the phase transitions of MFI-type zeolites, the small volume change and shape differences between the phases cannot be accounted assuming a fixed unit cell volume. Systems where adsorbed molecules induce rearrangement of the zeolite pores require host−host force fields specially designed for this purpose.

The simulations show that the long-range potentials (intraframework electrostatic and Lennard-Jones interactions) in flexible framework models intrinsically induce small but important changes in the atom positions of the zeolite and hence in the adsorption isotherms. The incompatibility of the partial charges of the zeolite atoms between host−host and guest−host interactions shows the need to consider both aspects for forcefields development.

The adsorption of alkylbenzenes in the pores of MFI-type zeolites represents confinement conditions. The confinement affects the physico-chemistry of the adsorbed molecules in different aspects.150,151 The confinement optimizes van der Waals interactions in zeolite cavities, involving a perturbation of the shape and electronic structure of the sorbate.25 This suggests that polarizability of sorbate molecules as well as the zeolite framework might have been overlooked.

Macroscopic behavior and properties of alkylbenzenes, such as VLE and critical points, can be well predicted with models that consider rigid molecules in gas and liquid phases.131 However, benzene rings are flexible.152 Laaksonen et al.153 reported that isolated benzene molecules can easily adopt non-planar conformations with torsion angles up to 10° at room temperature. Considering a C−C bond length of 1.4 Å, a C− C−C−C torsion angle of 10° in the aromatic ring induces a displacement of a C atom of approximately 0.24 Å. Such displacement is similar to the mean displacement of the zeolite atoms induced by the force fields for framework flexibility discussed in this work (see Table 1). This suggests that the intramolecular flexibility of aromatic molecules can be an important factor in the description of adsorption of aromatics in a zeolite pore.

Experimental work highlights challenges for an accurate description of the adsorption process. Data of adsorption of aromatics in MFI-type zeolites is scarce and not always consistent under the same temperature/pressure conditions. The experiments presented in this work show important differences with experiments from the literature performed decades ago. This suggests that experiments of adsorption of aromatics in MFI-type zeolites are highly dependent on the sample synthesis and detection methods. Such inconsistencies can also be related to diffusion limitations experienced by aromatic bulky molecules, such as m-xylene and o-xylene.154,155 The differences between experiments of adsorption of aromatics in MFI-type zeolites does not provide a clear overview on what to compare with simulations results, what to fit, or what to use as input for machine learning algorithms for forcefield development.

An accurate experimental description of the internal changes and crystal structure of the zeolite when varying pressure or temperature is needed. To the best of authors’ knowledge, detailed experimental insights on how the crystal structure changes hosting different aromatic molecules are not available. All this information is required to develop models able to reproduce and provide reliable molecular insights about the adsorption phenomena. Such requirements, pitfalls, and challenges underline that adsorption of aromatics in MFI-type zeolites is one of the most difficult systems to model. 4. CONCLUSIONS

The adsorption of n-heptane, ethylbenzene, and xylene isomers in MFI-type zeolites is computed using rigid and flexible zeolite frameworks. New experimental data of the adsorption of ethylbenzene in a MFI-type zeolite at 353 K is presented.

Figure 9.Adsorption isotherms of p-xylene at 373 K computed in the (a) Mono, (b) Ortho, and (c) Para structures. Closed circles and squares denote the experimental data from Wu et al.36and Song et al.,40respectively. Open triangles, upside down triangles, circles, and squares denote the simulations with the modified Nicholas105_model,

the modified Demontis103 _{model, the rigid structure with atom}

positions optimized at 0 K using the modified Nicholas model, and the rigid structure from experiments, respectively.

The experimental data shows significantly higher loadings than previously reported isotherms from the literature. Pore-size distributions (PSDs) of the MFI-type zeolite structures subject to three different host−host force field are computed. The PSDs show that the use of constant bond lengths induces displacements of the framework atoms that influence adsorption. Directly taking the bond lengths from the crystallographic structure minimizes this effect. The electro-static and LJ intraframework interactions induce displacements of the zeolite atoms that significantly affect the size of the pores and channels of the zeolite. The simulations of the adsorption of n-heptane in MFI-type zeolite at 303 K show a minor influence of framework flexibility for the computed isotherms compared to simulations using the rigid frameworks and experimental data. The simulations of adsorption of ethyl-benzene in MFI-type zeolite at 353 K show that the simulations with the modified Demontis model underestimate experimental loadings. The results suggest that the framework atom displacements using the modified Demontis model hinder the adsorption of aromatics in the zeolite. The use of the modified Nicholas model yields loadings closer to the experimental data. This is due to changes in the average zeolite structure caused by the intraframework interactions and not to frameworkflexibility. The vibrations of the zeolite atoms using the modified Nicholas model in the adsorption of ethylbenzene in MFI-type zeolites only play a role at high pressures/ loadings.

The simulations of adsorption of xylene isomers in MFI-type zeolites at 373 K showed that the influence of the flexibility is dependent on the framework. The use of the rigid framework and the modified Demontis model yields loadings close to the experimental isotherm for o-xylene and p-xylene. All simulations overestimate the experimental isotherm of m-xylene. p-Xylene in the Para structure is the only case where the flexible models show significantly lower loadings than in the rigid structure from experiments. The loadings in the rigid structure are higher than with frameworkflexibility models and overestimate the experimental loadings.

Using the considered host−host force fields, framework flexibility generates a new structure that is differently “rigid”. The flexible force fields produce a zeolite structure that vibrates around a new equilibrium configuration that has limited capacity to accommodate to a bulky guest molecule. The vibration of the zeolite atoms only plays role at high loadings, and the adsorption is mainly dependent on the average positions of the atoms. The intraframework interactions should be treated carefully as these interactions cause significant deviations from the experimental zeolite lattice. The adsorption of n-heptane in the MFI-type zeolite is not significantly influenced by the structure changes of the framework due to the forcefields for framework flexibility (see

Figure 4). The use of a zeolite structure with fixed atom

positions is appropriate when the molecule does notfit tightly in the zeolite pores. For aromatics, the influence of the force field for framework flexibility on the adsorption in MFI-type zeolites implies that the structural changes of the zeolite framework are relevant for molecules that fit tightly in the zeolite void spaces. The prediction of different loadings when a forcefield for framework flexibility is used compared to when a rigid structure is used is an artifact of the forcefield and not a re-accommodation of the framework atoms to a guest molecule. Forcefields for framework flexibility usually do not capture the physics behind the accommodation of the

framework atoms to a guest molecule. Obtaining a prediction of the loadings closer to the experiments is an overall effect of the host−host interactions and not guest interactions as desired. This implies that it is not possible to determine if one of the forcefields for framework flexibility performs best for the description of the adsorption of aromatics in MFI-type zeolites. Simulations of MOFs and other porous material considering framework flexibility use similar types of force fields.72,74

Thefindings of this work suggest that similar effects on the framework may be found for other classes of porous materials. The intraframework interactions of the modified Demontis model do not intrinsically change the zeolite structure. Using different spring constants in such a model could be of interest to investigate if the zeolite framework atoms can rearrange to accommodate guest molecules.

The simulations underline the need of new tailor-made force fields to model the zeolite flexibility for aromatics. Such force fields should focus on the local changes due to the presence of bulky guest molecules and not only vibrational behavior. As electrostatic interactions are important for adsorption purposes, the intraframework LJ interactions should also aim to balance the electrostatic interactions to preserve the atomic positions of the zeolite. There are many challenges and difficulties to model the framework flexibility and the adsorption of aromatics in MFI-type zeolites appropriately. An accurate experimental description of the internal changes and crystal structure of the zeolite when varying pressure or temperature is crucial. Data of adsorption of aromatics in MFI-type zeolites is scarce and not always consistent at the same temperature/pressure conditions. The variability on the experiments of adsorption of aromatics in MFI-type zeolites does not provide a clear overview on what to compare to the predictions of the simulations. This knowledge is required to develop models able to reproduce and provide reliable molecular insights about the adsorption phenomena. The simulations from this work show that force fields for frameworkflexibility should not be blindly applied to zeolites, and a general rethinking of the parametrization schemes for such models is needed.

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*

The Supporting Information is available free of charge at

https://pubs.acs.org/doi/10.1021/acs.jpcc.0c06096.

The crystal structures of MFI-type zeolites with atom positions optimized at 0 K using the Demontis103model, the Nicholas105model, and the model by Jeffroy et al.16 in CIF format (ZIP)

The parameters of the forcefields used in this work, a typical snapshot of the simulation of adsorption of ethylbenzene in MFI Para using the modified Nicholas model at 353 K and 2000 Pa, and the experimental loadings of ethylbenzene in Samples A and B of MFI-type zeolite at 353 K (PDF)

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Corresponding Author

Thijs J. H. Vlugt− Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, 2628 CB Delft, The Netherlands; orcid.org/0000-0003-3059-8712; Email:t.j.h.vlugt@tudelft.nl

Authors

Sebastián Caro-Ortiz − Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, 2628 CB Delft, The Netherlands

Erik Zuidema− Shell Global Solutions International B.V., 1030 BN Amsterdam, The Netherlands

Desmond Dekker− Shell Global Solutions International B.V., 1030 BN Amsterdam, The Netherlands

Marcello Rigutto− Shell Global Solutions International B.V., 1030 BN Amsterdam, The Netherlands

David Dubbeldam− Van ’t Hoff Institute of Molecular Sciences, University of Amsterdam, 1098 XH Amsterdam, The Netherlands; orcid.org/0000-0002-4382-1509

Complete contact information is available at:

https://pubs.acs.org/10.1021/acs.jpcc.0c06096 Notes

The authors declare no competingfinancial interest.

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The authors gratefully acknowledge financial support from Shell Global Solutions International B.V. This work was sponsored by NWO Exacte Wetenschappen (Physical Sciences) for the use of supercomputer facilities, withfinancial support from the Nederlandse Organisatie voor Wetenschap-pelijk Onderzoek (Netherlands Organization for Scientific Research, NWO). T.J.H.V. acknowledges NWO-CW for a VICI grant.

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